UNSOLVED PROBLEMS OF NOISE AND FLUCTUATIONS: UPoN 2005: Fourth International Conference on Unsolved Problems of Noise and Fluctuations in Physics, Biology, and High Technology

Mean Extinction Time for Birth‐Death Processes & Failure of the Fokker‐Planck Approximation
View Description Hide DescriptionWe consider extinction times for a class of birth‐death processes commonly found in applications where there is a control parameter that defines a threshold. Below the threshold the population quickly becomes extinct and above the threshold it persists for an exponentially long time. We derive an asymptotic expression for the mean time to extinction in the discrete population case for large values of the population scale, i.e., in the continuous population limit. The Fokker‐Planck (Markov diffusion process) approximation does not generally predict the true behavior of the extinction time for large values of the population scale. This is surprising because the continuum limit is precisely where it could be anticipated that the Fokker‐Planck approximation should be most accurate. Rather, it is valid only near the threshold. This constitutes an interesting example of the delicate relationship between discrete and continuum treatments of the same problem.

How Good Is Langevin?
View Description Hide DescriptionThe Langevin equation is universally applied to describe noise in physical systems of all kinds. In order to derive it, rather than postulating it, one has to introduce a noise source such as an environment or “reservoir”. The solution requires that at some initial time the reservoir is in equilibrium and uncorrelated with the system. This is unphysical and moreover, in the quantum mechanical case leads to inconsistencies. The way to overcome this anomaly is by considering the equilibrium of system and noise source combined. The resulting equations for the time dependent correlations between various operators can be computed. In order to find out whether the Langevin equation is able to reproduce the result we consider the explicitly solvable system of a harmonic oscillator in a harmonic bath. Conclusion: Langevin cannot describe quantum noise but belongs to the realm of mesoscopic physics.

Applications Of Stochastic Differential Equations In Electronics
View Description Hide DescriptionWe argue that the stochastic differential calculus of Itô is the best tool for the analysis of noise in electronic circuits. We begin by showing how the nodal and mesh equations of ordinary circuit analysis can be extended to model the effects of thermal fluctuations. This leads to a systematic method for formulating Langevin equations for electronic circuits. These can then be transformed into ordinary differential equations, allowing the calculation of noise power without the need to explicitly solve the stochastic differential equations.
We have encountered a difficult unsolved problem of noise, which arises when our technique is applied to the standard noise model for a MOSFET. The resulting equations are singular and do not yield to the usual algebraic manipulations. We do not appear to have enough independent equations for the number of (apparently) independent variables. Why is it so?

Full Counting Statistics And Shot Noise In Diffusive Mesoscopic Superconductors
View Description Hide DescriptionWe study shot noise in mesoscopic diffusive wires between a normal and a superconducting terminal. We particularly focus on the regime, in which the proximity‐induced reentrance effect is important. We will examine the difference between a simple Boltzmann‐Langevin description, which neglects induced correlations beyond the conductivity correction, and a full quantum calculation. In the latter approach, it turns out that two Andreev pairs propagating coherently into the normal metal are anti‐correlated for E ≲ E_{c} , where E_{c} = ℏD/L ^{2} is the Thouless energy.

The Role Of Noise In Quantum Communication
View Description Hide DescriptionIn quantum information and quantum computing, the carrier of information is a quantum system and information is encoded in its state. Secure communication schemes employ non‐orthogonal states that can not be discriminated with 100% probability of success. We briefly review various possible optimized state discrimination strategies since they provide a quantitative figure of merit for the acceptable noise level in quantum communication. We also report on recent results in two special areas. First, we consider discrimination between mixed quantum states. Second, we show that communication via completely unknown quantum states is possible and discuss programmable quantum state discriminators that accomplish this task optimally.

Nucleation Time Distribution In The Two‐Dimensional Ising Model With Spin‐Flip Dynamics
View Description Hide DescriptionThe distribution of nucleation times is studied for the two‐dimensional Ising model with spin‐flip dynamics in an external magnetic field. Direct simulation results for the nucleation times, spanning more than four orders of magnitude, are compared with theoretical predictions. Cluster free energies and effective transition rates for growth and shrinkage of clusters are determined directly from our simulations. The free energies so determined are well described by the classical Becker‐Döring expression, provided one uses an effective surface tension that exceeds the macroscopic surface tension by up to 20%. Within this framework there is good agreement between simulation results and theoretical predictions for the mean nucleation time.

Unsolved Problems of Surface Diffusion at Low Friction
View Description Hide DescriptionSurface transport and diffusion at low damping reveals a number of unexplained or at least not systematically explained behaviors. Here we present two problems that require further study for a full understanding. One involves motion on a random surface, the unresolved issue being the parameter regimes leading to subdiffusive, diffusive, and superdiffusive motions at intermediate times. The other involves the temperature dependence of maximal diffusion on a periodic surface in the presence of a constant external force.

Open Problems In Noise In NEMS
View Description Hide DescriptionNanoelectromechanical systems (NEMS) is a new technology which achieves its functionality by combining electrical transport with mechanical motion of nanoscopic bodies. The measured current‐voltage characteristics does not always yield sufficient information to uniquely identify the underlying charge transport mechanism, and thus different theoretical models may result in indistinguishable predictions for the IV‐characteristics. Therefore, the measurement of noise, and even the full counting statistics is viewed as an important step towards a more complete understanding of the dynamics of NEMS devices. While significant progress has been made in recent years in the theory of noise in NEMS, several open issues and challenges remain, both concerning the appropriate quantum mechanical equations to be used, their simplified semiclassical counterparts, and, finally, their numerical evaluation. We illustrate some of these issues using a quantum mechanical charge shuttle as a bench‐marking system.

Fluctuations In Electrohydrodynamic Instability
View Description Hide DescriptionElectrohydrodynamic Convection in Liquid Crystals (EHC) is a good system for the experimental study of spatio‐temporal chaos. Particularly interesting is the behavior of the Nematic in presence of weak turbulence where ordered and disordered states are mixed. In this case, the fluctuations of velocity and electric current, for instance, are typical fluctuations of a system far from equilibrium. Recently some authors have analyzed the amplitude of the fluctuations as function of the applied electric field and they present interesting interpretations provided by some theories. Although important results have been obtained by these authors, many aspects of the dynamical behavior have to be further analyzed as the role of some localized coherences inside the turbulence regions. The direct optical observation allows us to make a correspondence between fluctuations and patterns, providing important information for a theoretical interpretation.

Effective Temperature In Sheared Binary Systems
View Description Hide DescriptionWe study the dynamics of a binary system with a non conserved order parameter under the action of a plain shear flow in the large‐N limit. A phase transition is observed at a critical temperature T_{c} (γ). After a quench from a high temperature equilibrium state to a lower temperature T a non‐equilibrium stationary state is entered when T > T_{c} (γ), while aging dynamics characterizes the phases with T ⩽ T_{c} (γ). The behavior of the effective temperature T_{eff} is discussed. For T > T_{c} (γ) a non monotonous behavior is observed while, below T_{C} (γ), the usual result T_{eff} = ∞ of coarsening systems is found in the aging regime.

Shot Noise Spectrum Cut‐off in Schottky‐Barrier Diodes
View Description Hide DescriptionWe develop an analytical model for the shot‐noise spectral density of n^{+}n‐metal Schottky‐barrier diodes (SBDs). It is shown that the cut‐off of shot‐noise takes place in the frequency region corresponding to the resonance of carriers reflected from the Schottky‐barrier. The model is validated by comparison with Monte Carlo simulations of GaAs SBDs.

How Does One Describe A Time‐Varying Statistical Spectrum: Transforming Stochastic Differential Equations Into Phase‐Space
View Description Hide DescriptionWe address some fundamental issues regarding nonstationary stochastic processes. Among the questions we discuss are how one describes a nonstationary process and how one obtains a governing differential equation for it. We argue that a simplification occurs when one studies stochastic process in the time‐frequency phase space. This leads to a number of interesting questions. How can one obtain the equations of motion for reduced quantities such as the mean and variance of a nonstationary stochastic process? How can one define local stationarity? How can nonstationary stochastic systems be modeled from experimental data? Among other questions.

Renewal, Modulation and Blinking Quantum Dots
View Description Hide DescriptionA method of time series analysis based on the aging properties of renewal processes is introduced. The method compute the amount of renewal aging in a time series. It is shown that the method allows to distinguish between systems with a renewal dynamics from those driven by slow modulation of the parameters. The application of the method to Blinking Quantum Dots shows a maximum of renewal aging. This excludes the possibility of interpreting the dynamics as a slow modulation process and indicates a possible modelling approach in the renewal perspective.

Non‐Exotic Theory Of 1/f Noise As A Trace Of Infralow‐Frequency Fluctuations
View Description Hide DescriptionThis report is aimed at reviving the explanation of flicker‐noise observations as the result of spectral measurement of very low‐frequency but stationary narrow‐band fluctuations named as infralow‐frequency noise (ILF noise). Such a kind of the spectrum analyzer output takes place when the ILF‐noise correlation time is much longer than the analyzer reciprocal bandwidth. This result is valid for both analog and digital spectral measurements. The measured signal is proportional in this case to the mean square and not to the spectral density of the noise. The equilibrium temperature fluctuations and the defect‐motion as mechanisms of 1/f noise in metal films are reconsidered from this point of view. It is shown that the ILF‐noise approach allows to remove the main objection against temperature fluctuation model and difficulties within the defect‐motion model widely discussed in literature.

Noise In Nonohmic Regimes Of Disordered Systems
View Description Hide DescriptionWe present here a short review of mainly experimental properties of noise as disordered systems are driven into non‐ohmic regimes by applying voltages of few volts only. It is found that the noise does not simply follow the resistance in that the direction of change of noise could be opposite to that of resistance. It is discussed how this and other properties make the noise a complementary and incisive tool for studying complex systems, particularly its dynamic properties. Study of noise in non‐ohmic regimes in physical systems is rather in a nascent stage. Some of the open issues are highlighted.

Noise Activated Switching Between Dynamical States In A Nonlinear Micromechanical Oscillator
View Description Hide DescriptionWe explore fluctuation induced switching for a system that is far from equilibrium. The device under study is an underdamped micromechanical torsional oscillator driven into the nonlinear regime. Under a sufficiently strong periodic driving field, the oscillator possesses two stable dynamical states with different oscillation amplitudes within a certain range of driving frequencies. The oscillator is induced to switch from one dynamical state into the other by noise in the excitation. We demonstrate the activated behavior of escape from the high‐amplitude state to the low‐amplitude state by measuring the rate of transitions as a function of noise intensity.

Random Telegraph Signal In Si n‐MOSFETs: A Way Towards Single Spin Resonance Detection
View Description Hide DescriptionSingle spin detection is one of the most challenging tasks towards the realization of a solid‐state‐based quantum information processor. Spin‐dependent (SD) processes in the random telegraph signal (RTS) observed in silicon MOSFETs may lead to quantum bit read‐out. In addition, if successful, SD‐RTS will allow a direct identification and microscopic characterization of the trap responsible for the RTS. The experiment and its interpretation present a number of technical difficulties and open issues.. We discuss our experimental results towards a deep understanding of spin‐dependent RTS aiming at shading light on several open questions related to the influence of the microwave field, the static magnetic field, and the effective temperature of the electron gas.

High‐Frequency Noise In AlGaN/GaN Heterostructures
View Description Hide DescriptionHigh‐frequency noise (10–100MHz) was studied in undoped AlGaN/GaN high electron mobility transistor heterostructures. Two equivalent approaches, noise temperature and resistance fluctuations, were considered for the data analysis. Three possible mechanisms of noise origin were considered and investigated in detail. These include thermal noise, diffusive noise of hot electron and generation‐recombination (G‐R) noise. The results of our analysis show a dominant influence of G‐R noise, which contains two components with different temperature dependences demonstrating the different physical origins of the noise. It is concluded that the concentration fluctuations of electrons on the first quantum level of the quantum well and scattering of the electrons in the barrier layer play a very important role in the noise phenomena.

On Bunching Of Fractionally‐Charged Quasiparticles
View Description Hide DescriptionShot noise measurements are an important tool for characterizing the charge of current carriers and the correlation among them. Most notable recently was the verification that quasiparticles in the Fractional Quantum Hall (FQH) regime have fractional charge q=e/n, with e the charge of the electron, n an odd integer,:and v=p/n the fractional filling of the first Landau level (such as 1/3, 2/5, 3/7, etc.). We investigate here the interaction of quasiparticles with a strong back scatterer and find unexpected results. When a weak back scatterer (with transmission t≈1) is introduced in the path of an otherwise noiseless current of quasiparticles (a fully occupied beam), stochastic partitioning and noise proportional to the quasiparticles charge appear. Specifically, at v=1/3 noise corresponding to a partitioned charge q=e*=e/3 is measured. However, this charge increases monotonically as backscattering becomes stronger — approaching q=e for t→0. In other words, only electrons (or, alternatively, three bunched quasiparticles) are found to tunnel through high potential barriers when impinged by a noiseless current of quasiparticles. Here we show that the partitioned charge, or the bunching of quasiparticles, after a strong back scatterer, depends on the average state occupation of the impinging current (the dilution of the quasiparticles beam). In the limit of a very dilute impinging current, when quasiparticles arrive one by one, bunching ceases altogether and the transferred charge approaches q=e*=e/3. These surprising results, not yet understood, prove that sparse quasiparticles, with charge e*=e/3, can tunnel through high potential barriers, originally thought to be opaque.